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Гребнерове базе за многострукости застава и примене

Gröbner bases for flag manifolds and applications.

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2015
Disertacija3611.pdf (1.408Mb)
Radovanovic_Marko_S.pdf (1008.Kb)
Author
Radovanović, Marko S.
Mentor
Petrović, Zoran
Committee members
Lipkovski, Aleksandar
Malešević, Branko
Đanković, Goran
Prvulović, Branislav
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Abstract
о Бореловом опису, целобројна и мод 2 кохомологија многостру- кости застава дата је као полиномијална алгебра посечена по одређе- ном идеалу. У овом раду, Гребнерове базе за ове идеале добијене су у случају комплексних и реалних Грасманових многострукости, као и у случају реалних многострукости застава F(1,...,1; 2,...,2,k,n)...
By Borel's description, integral and mod 2 cohomology of ag manifolds is a polynomial algebra modulo a well-known ideal. In this doctoral dissertation, Gr obner bases for these ideals are obtained in the case of complex and real Grassmann manifolds, and real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n). In the case of Grassmann manifolds, Gr obner bases are applied in the study of Z- cohomology of complex Grassmann manifolds. It is well-known that, besides Borel's description, this cohomology can be characterized in terms of Schubert classes. By establishing a connection between this description and Gr obner bases that we obtained, a new recurrence formula that can be used for calculating (all) Kostka numbers is derived. Using the same method for the small quantum cohomology of Grassmann manifolds (instead of the classical), these formulas are improved. In the case of real ag manifoldsF(1,...,1; 2,...,2,k,n), Gr obner bases are used to obtain new results on the immersions and em...beddings of these manifolds, and for the calculation of the cup-length of some manifolds of this type.

Faculty:
Универзитет у Београду, Математички факултет
Date:
23-07-2015
Keywords:
Гребнерове базе / Gr obner bases / cohomology of ag manifolds / quantum cohomology / symmetric functions / Kostka numbers / cup-length / Schubert calculus / Chern classes / Stiefel-Whitney classes / immersions / кохомологија многострукости застава / квантна кохомологија / симетричне функције / Косткини бројеви / кохо- молошка дужина / Шубертов раqун / Чернове класе / Штифел-Витнијеве класе / имерзије
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Handle
https://hdl.handle.net/21.15107/rcub_nardus_5724
URI
https://nardus.mpn.gov.rs/handle/123456789/5724
http://eteze.bg.ac.rs/application/showtheses?thesesId=3071
https://fedorabg.bg.ac.rs/fedora/get/o:11333/bdef:Content/download
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